Adaptive Inverse Iterative Learning Control

Iterative learning control (ILC) creates methods of learning from experience in order to perform high speed or high precision motions not otherwise possible with feedback control. This work aims at tracking problems that are very short, i.e. with a time duration that is short compared to the settling time of the system. A convolution sum model, or Toeplitz matrix model is used. Methods are developed to identify the Toeplitz matrix from input-output data. Rank one updates are suggested for the adaptive model updates during the learning. Tikhonov regularization is suggested to handle the usually ill-conditioned problem of finding the control update from the model, but quadratic cost learning control iterations are an alternative. Some concepts for regularizing the identification of an inverse model are suggested.